If one particular thinking strategy stands out about creative genius, it is the ability to make juxtapositions that elude mere mortals. Call it a facility to connect the unconnected that enables them to see relationships to which others are blind. They set their imagination in motion by using unrelated stimuli and forcing connections with their subject.

Leonardo Da Vinci discovered that the human brain cannot deliberately concentrate on two separate objects or ideas, no matter how dissimilar, without eventually forming a connection between them. No two inputs can remain separate in your mind no matter how remote they are from each other.

In tetherball, a ball is fastened to a slender cord suspended from the top of a pole. Players bat the ball around the pole, attempting to wind its cord around the pole above a certain point. Obviously, a tethered ball on a long string is able to move in many different directions, but it cannot get away from the pole. If you whack at it long enough, eventually you will wind the cord around the pole. This is a closed system. Like the tetherball, if you focus on two subjects for a period of time, you will see relationships and connections that will trigger new ideas and thoughts that you cannot get using your usual way of thinking.

Da Vinci’s knack to make remote connections was certainly at the basis of Leonardo’s genius to form analogies between totally different systems. He associated the movement of water with the movement of human hair, thus becoming the first person to illustrate in extraordinary detail the many invisible subtleties of water in motion. His observations led to the discovery of a fact of nature which came to be called the Law of Continuity. When you make a connection between two unrelated subjects, your imagination will leap to fill the gaps and form a whole in order to make sense of it.

Suppose you are watching a mime impersonating a man taking his dog out for a walk. The mime’s arm is outstretched as though holding the dog’s leash. As the mime’s arm is jerked back and forth, you “see” the dog straining at the leash to sniff this or that. The dog and the leash become the most real part of the scene even though there is no dog or leash. In the same way, when you make connections between your subject and something that is totally unrelated, your imagination fills in the gaps to create new ideas. It is this willingness to use your imagination to fill in the gaps that produces the unpredictable idea. This is why Einstein claimed that imagination is more important than knowledge.

Conceptual blending is central to human thought and imagination, and evidence of this can be found in human language, art, science, industry and in a wide range of human activities. Think about the connections, if any, between a beehive and de-icing power lines during ice storms. How can a beehive be the clue to a solution? Engineers working for a power company in the northwest were struggling with the problem of how to de-ice power lines during ice storms so they don’t collapse from the weight of the ice.

The conventional approaches to the problem were proving to be very expensive and inefficient. It is not possible to think unpredictably by looking harder and longer in the same direction. When your attention is focused on a subject, a few patterns are highly activated in your brain and dominate your thinking. These patterns produce only predictable ideas no matter how hard you try. In fact, the harder you try, the stronger the same patterns become. If, however, you change your focus and think about something that is not related, different, unusual patterns are activated. If one of these newer patterns relates to one of the first patterns, a connection will be made. This connection will lead to the discovery of an original idea or thought. This is what some people call “divine” inspiration.

This is what the engineers did. Using a technique from my book Thinkertoys on how to find and force connections between a challenge and random stimuli, they randomly picked the subject “Beehives.” Then they listed a variety of things that are associated with beehives and listed them. Included were

Bees colonize and live in beehives.

Beehives are used to store honey and pollen.

Honey is a sweet food.

Ancient Egyptians used honey to embalm corpses.

Beehives are a favorite food of bears.

Bears will climb trees to get the hive or shake the tree to make it fall. Vibrations make them fall. Bees communicate with each other with vibrating wings. The associations with beehives and vibrating wings and bears vibrating trees got them all interested in the principle of vibrational motion as the answer. Vibrate the ice off the power lines. But how?

How can we use vibration to help solve the problem? In addition, bears retrieve beehives by shaking trees or by climbing them. Shaking would cause the power lines to vibrate and shake off the ice. A bear climbing a power pole would shake the pole and vibrate power lines as well. Vibration became the principle they focused on. How can they vibrate the power lines economically? One engineer remarked that bees can hover like helicopters. That reminded him of the powerful downwash from a helicopter’s blades. The answer is to hover choppers over the lines and the downwash will vibrate the ice off the lines. This proved to be the most efficient and economical solution to the problem.